It's all up to what you want of course. Though I can't see why you'd fly all the way around the world to Japan and then go to an Americana theme park. Why not see Japan? There are Japanese theme parks as well, like Edo Wonderland in Nikko, and Fuji Q Highland.
http://edowonderland.net/en/https://www.japan-guide.com/e/e6918.htmlPerhaps see Disney Sea if you like, since it is unique.
Honestly though, with 10 days and at least a couple of them going to theme parks, I wouldn't bother going down to Kansai at all, unless you are really sure you'll never go back to Japan again ever, or at least for the near future. There are loads of places in the Tokyo area.
Have you looked through the site's page on the city, as well as the official city tourist guide, etc?
http://www.japan-guide.com/e/e2164.htmlhttp://www.gotokyo.org/en/index.htmlhttps://goo.gl/tAECfMSeeing the Sensoji Temple and Meiji Shrine (and don't skip the Meiji Gyoen Garden there also) is pretty much de rigueur for any first timer. There are close to a dozen beautiful historic gardens in the city, some with a history going back centuries.
https://goo.gl/tAECfMPlus lots of places for great city views - the Sky Tree and Mori Bldg are some of the best but also rather pricey. If you want to save some money, there are also many good places that are free.
http://supermerlion.com/10-free-tokyo-city-views/
One of the more recent trippy places is the TeamLab Borderless digital museum:
https://borderless.teamlab.art/If you are set on going down to Kansai as well, then just one day in Kyoto is severely shortchanging the place and if you are already seeing Tokyo, there is no real need to spend any day time hours there. The city comes to life in the evening anyway, and there is more to enjoy, like Dotonbori, Shinsekai, and the city views from atop the Umeda Sky Bldg and Abeno Harukas Bldg.
http://goo.gl/XE5R94Putting in a half day at least to see Nara is also very worthwhile - the Todaiji Great Buddha will be something you will never forget for the rest of your life.
http://bit.ly/1Rhxg0EAnd if you want to see a real castle, skip Osaka "Castle" entirely - it is not a castle, nor even a reconstruction. It's a cube museum with a castle facade thrown over it. Take half a day and go see Himeji Castle and the Kokoen Garden - both are excellent. Get the combo ticket, and one is virtually free.
https://goo.gl/65ZtRiSo if you split your time 50/50 between Tokyo and Kansai, you could do 4 days in Kyoto (you could spend 4 months there and not begin to see it all) with half a day for Nara and half a day for Himeji (though better on different days), and see Osaka after a day of sightseeing in Kyoto. On another evening, you could also go and see Kobe - Mt Rokko, Mt Maya, the Port Tower, Chinatown, etc.
If you are concerned about activities for your kids in Kyoto, remember also there is more than just temples and shrines - the Toei Eigamura studios, monkey park, railway museum, Sagano Scenic Railway & Hozugawa river cruise, manga museum, Murin-an home/garden, etc.
http://www.japan-guide.com/e/e2158.htmlhttps://goo.gl/knQtMgAlso you mentioned seeing the cherry blossoms - you can find a collection of popular places at
https://www.japan-guide.com/e/e2011_where.htmlbut I suggest you get out of the big cities to see them, unless you want to "enjoy" them like this:
https://imgur.com/V7xJXfa
